"""
Project Euler Problem 11: https://projecteuler.net/problem=11

What is the greatest product of four adjacent numbers (horizontally,
vertically, or diagonally) in this 20x20 array?

08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
"""

# _*_ conding:UTF-8 _*_
'''
@author = Kuperain
@email = kuperain@aliyun.com
@IDE = Thonny Python3.7.3
@creat_time = 2022/5/6
'''

DATA = '''
08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
'''

DATA_Array = '[[' + DATA.strip().replace('\n', '],[').replace(' ', ',') + ']]'
DATA_Array = DATA_Array.replace(',0', ',').replace('[0', '[')
DATA_Array = eval(DATA_Array)

# **********************************************************************


def product_of_k_adjacent_numbers(i: int, j: int, A: list, k: int = 4) -> int:
    '''
    for A(i,j) in array A(NxN), 
    compute greatest product of four adjacent numbers (horizontally, vertically, or diagonally)
    '''
    
    n = len(A)  # size of array
    
    prodcut = lambda x,y : x*y
    distance_up    = i + 1  # i=3, has 4 number up
    distance_down  =  n - i
    distance_right = n - j
    distance_left  = j + 1
    
    # there are 2*2*2*2 = 16 cases, 8 directions(degree 0, 45, 90, 135, 180, 225, 270, 315, clockwise)
    from functools import reduce
    product_0   = 0 if distance_up    < k else reduce(prodcut, [A[i-p][j] for p in range(k)])
    product_180 = 0 if distance_down  < k else reduce(prodcut, [A[i+p][j] for p in range(k)])
    product_90  = 0 if distance_right < k else reduce(prodcut, [A[i][j+p] for p in range(k)])
    product_270 = 0 if distance_left  < k else reduce(prodcut, [A[i][j-p] for p in range(k)])
    product_45  = 0 if distance_up    < k or distance_right < k  else reduce(prodcut, [A[i-p][j+p] for p in range(k)])
    product_135 = 0 if distance_down  < k or distance_right < k  else reduce(prodcut, [A[i+p][j+p] for p in range(k)])
    product_225 = 0 if distance_down  < k or distance_left  < k  else reduce(prodcut, [A[i+p][j-p] for p in range(k)])
    product_315 = 0 if distance_up    < k or distance_left  < k  else reduce(prodcut, [A[i-p][j-p] for p in range(k)])
    
    
    return max(product_0, product_45, product_90, product_135, product_180, product_225, product_270, product_315)


def solution(A: list = DATA_Array, k: int = 4) -> int:
    
    n = len(A)
    
    res = 0
    x, y = 0, 0
    for i in range(n):
        for j in range(n):
            tmp = product_of_k_adjacent_numbers(i, j, A, k)
            if tmp > res:
                res = tmp
                x, y = i, j
                
    return res, (A[x][y], x, y)

if __name__ == "__main__":
    import doctest
    doctest.testmod(verbose = False)
    
    print(f"solution() = {solution()}")
    # solution() = (70600674, (89, 12, 6))


    


